Optimality conditions for nonlinear semidefinite programming via squared slack variables View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-06-25

AUTHORS

Bruno F. Lourenço, Ellen H. Fukuda, Masao Fukushima

ABSTRACT

In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the correspondence between Karush-Kuhn-Tucker points and regularity conditions for the general NSDP and its reformulation via slack variables. Then, we obtain a pair of “no-gap” second-order optimality conditions that are essentially equivalent to the ones already considered in the literature. We conclude with the analysis of some computational prospects of the squared slack variables approach for NSDP. More... »

PAGES

177-200

References to SciGraph publications

  • 1988-05. An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems in MATHEMATICAL PROGRAMMING
  • 1997-04. First and second order analysis of nonlinear semidefinite programs in MATHEMATICAL PROGRAMMING
  • 1999. Numerical Optimization in NONE
  • 2011-09-26. Elementary Optimality Conditions for Nonlinear SDPs in HANDBOOK ON SEMIDEFINITE, CONIC AND POLYNOMIAL OPTIMIZATION
  • 2003-02. A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization in MATHEMATICAL PROGRAMMING
  • 1990-01. Metric regularity, tangent sets, and second-order optimality conditions in APPLIED MATHEMATICS & OPTIMIZATION
  • 2000-06. Optimality conditions for nonconvex semidefinite programming in MATHEMATICAL PROGRAMMING
  • 1980-01. Test examples for nonlinear programming codes in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1995-03-01. Problems of distance geometry and convex properties of quadratic maps in DISCRETE & COMPUTATIONAL GEOMETRY
  • 2000. The Geometry of Semidefinite Programming in HANDBOOK OF SEMIDEFINITE PROGRAMMING
  • 2016-02-29. The Use of Squared Slack Variables in Nonlinear Second-Order Cone Programming in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2004-12-29. Local Minima and Convergence in Low-Rank Semidefinite Programming in MATHEMATICAL PROGRAMMING
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10107-016-1040-4

    DOI

    http://dx.doi.org/10.1007/s10107-016-1040-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1021000634


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